Add to ORKGWe develop a Thurston-like theory to characterize geometrically finite rational maps, then apply it to study pinching and plumbing deformations of rational maps. We show that in certain conditions the pinching path converges uniformly and the quasiconformal conjugacy converges uniformly to a semi-conjugacy from the original map to the limit. Conversely, every geometrically finite rational map with parabolic points is the landing point of a pinching path for any prescribed plumbing combinatorics. * 2010 Mathematics Subject Classification: 37F20, 37F45 supported by NSFC grant no. 11125106
Every Thurston map $f\colon S^2\rightarrow S^2$ on a $2$-sphere $S^2$ induces a pull-back operation ...
One fundamental theorem in the theory of holomorphic dynamics is Thurston's topological characteriza...
One fundamental theorem in the theory of holomorphic dynamics is Thurston's topological characteriza...
In this paper, we study hyperbolic rational maps with finitely connected Fatou sets. We construct mo...
In this thesis we investigate degeneration of rational maps and generation of parabolic cycles. Ther...
AbstractIn 1980's, Thurston established a combinatorial characterization for post-critically finite ...
We give a topological characterization of rational maps with disconnected Julia sets. Our results ex...
We apply Thurston's characterization of postcritically finite rational maps as branched coverings of...
A general approach is proposed to prove that the combination of expansion with bounded distortion yi...
Abstract. We describe an algorithm for distinguishing hyperbolic compo-nents in the parameter space ...
A rational map f is called geometrically finite if every critical point contained in its Julia set i...
AbstractIn 1980's, Thurston established a combinatorial characterization for post-critically finite ...
The traditional view in numerical conformal mapping is that once the boundary correspondence functio...
Abstract. We show that two rational maps which are K-quasiconformally combinatorially equivalent are...
One fundamental theorem in the theory of holomorphic dynamics is Thurston's topological characteriza...
Every Thurston map $f\colon S^2\rightarrow S^2$ on a $2$-sphere $S^2$ induces a pull-back operation ...
One fundamental theorem in the theory of holomorphic dynamics is Thurston's topological characteriza...
One fundamental theorem in the theory of holomorphic dynamics is Thurston's topological characteriza...
In this paper, we study hyperbolic rational maps with finitely connected Fatou sets. We construct mo...
In this thesis we investigate degeneration of rational maps and generation of parabolic cycles. Ther...
AbstractIn 1980's, Thurston established a combinatorial characterization for post-critically finite ...
We give a topological characterization of rational maps with disconnected Julia sets. Our results ex...
We apply Thurston's characterization of postcritically finite rational maps as branched coverings of...
A general approach is proposed to prove that the combination of expansion with bounded distortion yi...
Abstract. We describe an algorithm for distinguishing hyperbolic compo-nents in the parameter space ...
A rational map f is called geometrically finite if every critical point contained in its Julia set i...
AbstractIn 1980's, Thurston established a combinatorial characterization for post-critically finite ...
The traditional view in numerical conformal mapping is that once the boundary correspondence functio...
Abstract. We show that two rational maps which are K-quasiconformally combinatorially equivalent are...
One fundamental theorem in the theory of holomorphic dynamics is Thurston's topological characteriza...
Every Thurston map $f\colon S^2\rightarrow S^2$ on a $2$-sphere $S^2$ induces a pull-back operation ...
One fundamental theorem in the theory of holomorphic dynamics is Thurston's topological characteriza...
One fundamental theorem in the theory of holomorphic dynamics is Thurston's topological characteriza...